2-5/x=3/x^2

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Solution for 2-5/x=3/x^2 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

2-(5/x) = 3/(x^2) // - 3/(x^2)

2-(5/x)-(3/(x^2)) = 0

2-5*x^-1-3*x^-2 = 0

t_1 = x^-1

2-3*t_1^2-5*t_1^1 = 0

2-3*t_1^2-5*t_1 = 0

DELTA = (-5)^2-(-3*2*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+5)/(-3*2) or t_1 = (5-49^(1/2))/(-3*2)

t_1 = -2 or t_1 = 1/3

t_1 = -2

x^-1+2 = 0

1*x^-1 = -2 // : 1

x^-1 = -2

-1 < 0

1/(x^1) = -2 // * x^1

1 = -2*x^1 // : -2

-1/2 = x^1

x = -1/2

t_1 = 1/3

x^-1-1/3 = 0

1*x^-1 = 1/3 // : 1

x^-1 = 1/3

-1 < 0

1/(x^1) = 1/3 // * x^1

1 = 1/3*x^1 // : 1/3

3 = x^1

x = 3

x in { -1/2, 3 }

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